Two applications of the Gosper algorithm

主讲人：穆彦平 天津理工大学教授

时间：2024年7月11日15：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：穆彦平，天津理工大学教授，2006年博士毕业于南开大学，主要的研究方向是符号计算，在Journal of Symbolic Computation, The Ramanujan Journal, Journal of Number Theory等杂志上发表多篇论文。

内容介绍：Firstly, we present a method for constructing simple Bailey pairs based on the q-Gosper algorithm. We illustrate this method by determining Gosper-summable q-hypergeometric terms with specific forms. As applications, we derive some summation and transformation formulas for q-series. Secondly, we utilize the extended Zeilberger algorithm to construct WZ (Wilf-Zeilberger) pairs. To illustrate the process, we start with identity (H.1) as provided by Van Hamme. We find eleven WZ pairs. Using these WZ pairs, we derive various summation formulas, transformation formulas, and supercongruences. Additionally, we present a strategy for constructing q-WZ pairs from WZ pairs and provide two q-analogues of (H.1).